{
  "abstract": "We show that if a contractible Stein manifold $X$ with the density property admits a proper holomorphic embedding into $\\mathbb{C}^k$, then $X \\times \\mathbb{C}^k$ is biholomorphic to $\\mathbb{C}^{n+k}$ with $n=\\dim X$. We also prove that McLean's exotic affine variety $K_n$, $n\\ge4$, a smooth contractible affine variety which is not biholomorphic to $\\mathbb{C}^n$, has the density property. Hence for $n \\ge 4$ there exist an integer $m \\in \\{ n, \\dots, 2n\\}$ and an affine variety $X$ such that $X \\times \\mathbb{C}$ is biholomorphic to $\\mathbb{C}^{m+1}$ and $X$ is not biholomorphic to $\\mathbb{C}^m$. This settles the Holomorphic Cancellation Problem in the negative. We also construct holomorphic actions of $\\mathbb{C}^*$ and finite cyclic groups on complex Euclidean spaces that are not topologically conjugate to linear actions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12581",
  "author_total": 1,
  "authors": [
    {
      "name": "Gaofeng Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ct5rgdx3pkef.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12581",
  "fulltext_url": null,
  "id": "1ct5rgdx3pkef",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12581",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7221569089",
  "pdf_url": "https://arxiv.org/pdf/2610.12581",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ct5rgdx3pkef.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.12581",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12581"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Counterexample to the Holomorphic Cancellation Problem",
  "title_text": "A Counterexample to the Holomorphic Cancellation Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/1ct5rgdx3pkef",
  "venue": "arXiv",
  "versions": []
}